Abstract
A membership function may be concave-shaped or convex-shaped. In this chapter, first, concave and convex membership values are analyzed and, in practice, commonly used approaches for solving an fuzzy multi-objective decision-making (FMODM) problem are briefly reviewed. Then, some proposition and remarks are presented to solve a quasi-concave FMODM problem. The proposed method can directly solve a quasi-concave FMODM problem by using standard LP techniques.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Abdelaziz, F.B., Enneifar, L., and Martel, J.M., 2004, A multiobjective fuzzy stochastic program for water resources optimization: The case of lake management, INFOR, 42: 201-215.
Biswal, M.P., 1997, Use of projective and scaling algorithm to solve multi-objective fuzzy linear programming problems, The Journal of Fuzzy Mathematics, 5: 439-448.
Hannan, E.L., 1981a, Linear programming with multiple fuzzy goals, Fuzzy Sets and Systems, 6: 235-248.
Hannan, E.L., 1981b, On fuzzy goal programming, Decision Sciences, 12: 522-531.
Inuiguchi, M., Ichihashi, H., and Kume, Y., 1990, A solution algorithm for fuzzy linear programming with piecewise linear membership functions, Fuzzy Sets and Systems, 34: 15-31.
Lai, Y.J., and Hwang, C.L., 1994, Fuzzy Multiple Objective Decision Making, Springer-Verlag, New York.
Li, H.L., 1996, Technical note: An efficient method for solving linear goal programming problems, Journal of Optimization Theory and Applications, 90: 465-469.
Li, H.L., and Yu, C.S., 1999, Comments on “fuzzy programming with nonlinear membership functions …,” Fuzzy Sets and Systems, 101: 109-113.
Mjelde, K.M., 1983, Fractional resource allocation with S-shaped return functions, Journal of Operational Research Society, 34(7): 627-632.
Nakamura, K., 1984, Some extensions of fuzzy linear programming, Fuzzy Sets and Systems, 14: 211-229.
Narasimhan, R., 1980, Goal programming in a fuzzy environment, Decision Sciences, 11: 325-336.
Romero, C., 1994, Handbook of Critical Issues in Goal Programming, Pergamon Press, New York.
LINGO 9.0, 2005, LINDO System Inc., Chicago.
Simon, H.A., 1960, Some further notes on a class of skew distribution functions, Information and Control, 3: 80-88.
Yang, T., Ignizio, J.P., and Kim, H.J., 1991, Fuzzy programming with nonlinear membership functions: piecewise linear approximation, Fuzzy Sets and Systems, 41: 39-53.
Yu, C.S., and Li, H.L., 2000, Method for solving quasi-concave and non-concave fuzzy multi-objective programming problems, Fuzzy Sets and Systems, 109: 59-82.
Yu, C.S., 2001, A Method For Solving Quasi-Concave Or General Non-Concave Fuzzy Multi-Objective Programming Problems And Its Applications In Logistic Management, Marketing Strategies, And Investment Decision-Making, National Science Council of R.O.C., Taipei.
Zimmermann, H.J., 1976, Description and optimization of fuzzy systems, International Journal of General Systems, 2: 209-215.
Zimmermann, H.J., 1981, Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1: 45-55.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer Science + Business Media, LLC
About this chapter
Cite this chapter
Yu, CS., Li, HL. (2008). Quasi-Concave and Nonconcave FMODM Problems. In: Kahraman, C. (eds) Fuzzy Multi-Criteria Decision Making. Springer Optimization and Its Applications, vol 16. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-76813-7_14
Download citation
DOI: https://doi.org/10.1007/978-0-387-76813-7_14
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-76812-0
Online ISBN: 978-0-387-76813-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)